Attainable superheating of solutions of cryogenic liquids

The kinetics of spontaneous boiling-up of superheated binary solutions of cryogenic liquids is studied. Within the framework of the Kramers-Zeldovich method, an expression is obtained for the steady state rate of homogeneous nucleation in a solution that takes into account free-molecular and diffusion regimes of the substance supply to a growing bubble. Viscous and inertial forces are also taken into account in the study of the nucleus growth dynamics. The work of critical nucleus formation is determined within the framework of the Gibbs and van der Waals capillarity theories. The dependence of the surface tension of critical bubbles in the solution on their size is investigated. The temperature of attainable superheating and nucleation rates in superheated solutions of cryogenic liquids with complete or partial solubility of the components are determined by a method of lifetime measurement. The experiments were conducted in a wide range of pressures and solution concentrations. The measurement results are compared with the theory of homogeneous nucleation taking or not taking into account the size effect in nucleation. It has been found that, by taking into account the size dependence of the surface tension of a nucleus, better agreement between the theory and experiment is obtained. The boundary of essential instability of the solution, that is, the diffusion spinodal, is computed.     

Classical theory of homogeneous nucleation in superheated liquids and its experimental verification

This work summarizes the cycle of investigations devoted to determination of the character of superheated liquid boiling-up in a glass capillary at the boundary of the attainable superheating. The brief history of studies is followed by a brief introduction into the theory of homogeneous nucleation. The result of the targeted experiments determining stationarity of a random process of a supercritical embryo generation is considered. From the experiments it may be concluded that the process is unsteady. Based on a large selection of life spans of superheated liquids, the authors have made parametric and nonparametric evaluations of the functions of distribution and dependence of boiling-up frequency on time. The comparison of the obtained results with exponential distribution shows significant differences that also prove the nonstationarity of the studied random process. Special experiments and calculations for evaluation of homogeneity of the superheated liquid boilingup at the boundary of attainable superheating are considered. It is shown that in the experiments with glass capillary, the boiling-up occurs on the wall. As the most convincing evidence of heterogeneity of the superheated liquid boiling-up in a glass capillary the authors provide the results of high-speed video filming in a silylated and clean capillaries.     

Experimental testing of liquid boiling-up homogeneity near the boundary of the attainable superheating

Results of measured average expectancy time of n-pentane and n-hexane boiling-up to the boundary of attainable superheating are presented. Experiments have been carried out in glass capillaries with substantially decreasing value of the superheated liquid volume for the preset metastable state (p, T = const). Obtained data fail to prove correlation 1 JVῑ = following from the condition of homogeneity and stationarity of the random process resulting in the superheated liquid boiling-up (J is the frequency of homogenous nucleation, V is the volume of the superheated liquid, ῑ is the average life time). Thus, experiments on superheated liquid boiling-up kinetics bound with measurements of average life time in glass capillaries cannot serve a proof of the validity of classical theory of nucleation for superheated liquids since one of the ground conditions — boiling-up homogeneity — is not met.     

Crystal nucleation of colloidal suspensions under shear

We use Brownian dynamics simulations in combination with the umbrella sampling technique to study the effect of shear flow on homogeneous crystal nucleation. We find that a homogeneous shear rate leads to a significant suppression of the crystal nucleation rate and to an increase of the size of the critical nucleus. A simple, phenomenological extension of classical nucleation theory accounts for these observations. The orientation of the crystal nucleus is tilted with respect to the shear direction.     

Thermodynamics of nucleation in an internal oxide getter in silicon

Nucleation of precipitates of silicon dioxide is studied theoretically within the framework of the classical theory of nucleation. Elastic stresses, accompanying nucleation, are taken into account under the assumption that the nucleus and matrix are incoherent and the silicon is elastically isotropic. The results of a numerical calculation of the form and dimensions of the critical nucleus, the free energy of its formation, and the rate of nucleation as a function of the annealing temperature in the range 773–1473 K for oxygen concentrations in the starting single crystal of (0.4–1.4)·10¹⁸ cm^–3 are presented. It is shown that homogeneous nucleation of precipitates is, in principle, possible. The magnitude of the specific free energy of the interphase boundary is estimated based on the data obtained.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 25–29, August, 1988.     

Homogeneous Nucleation

Significant progress has been made in recent years in measuring homogeneous nucleation rates in a variety of liquid–vapor and liquid–solid transitions. These studies have revealed serious shortcomings of classical nucleation theory. New theoretical work and simulation studies of simplified model systems have provided a better understanding of homogeneous nucleation, but many challenges remain. This article summarizes some recent developments, with an emphasis on the field-theoretic approach pioneered by Cahn and Hilliard in their study of nucleation in a two-component incompressible fluid in 1959.     

Computer simulation of heterogeneous nucleation on curved surfaces using a simplified string method combined with phase-field simulations

We show how the combination of string method with the phase-field approach can be extended from simulations of homogeneous nucleation to heterogeneous nucleation. From these simulations, it is possible to directly obtain nucleation barriers for heterogeneous nucleation on arbitrary surfaces as well as information about the size and shape of the critical nucleus. We test the method by comparing the dependence of the nucleation barrier for heterogeneous nucleation on concave and convex surfaces on the surface curvature obtained from three-dimensional phase-field simulations with predictions from classical nucleation theory and find good agreement between them.     

Thermodynamics of supersaturated vapor nucleation on molecular condensation nuclei

A key problem in the theory of a supersaturated vapor nucleation on molecular condensation nuclei (namely, the work of formation and the equilibrium concentrations of clusters) is considered. To calculate these quantities using the structural models of clusters, which are better suited for this purpose than the classical droplet model, we derive the equation connecting the work of transfer of a molecular condensation nucleus from the gas phase to a homogeneous cluster with a change in the number of contacts between molecules, occurring in the course of this transfer, and with the work of rupture of individual contacts.     

Molecular dynamics simulation of homogeneous nucleation of KBr cluster

We perform molecular dynamics simulations to study the homogeneous nucleation in the freezing of molten potassium bromide clusters. The nucleation rates tend to decrease with increasing cluster size and temperature. The solid-liquid interfacial free energy σ_sl of 42.4-52.3 mJ/m² is close to the values predicted by Turnbull's relation and comparable to the experimental observation by Buckle and Ubbelohde. It is interesting to find that there is no cluster size effect on the critical nucleus size. Critical nucleus sizes inferred from classical nucleation theory are of 6.5-20.7 K⁺Br⁻ ionic pairs in the temperature range of 400-600 K. The critical nucleus size at bulk MD freezing temperature obtained by extrapolation is about 45 K⁺Br⁻ ionic pairs, which is comparable to the experimental value of NaCl.     

Kinetic pathways for the isotropic-nematic phase transition in a system of colloidal hard rods: a simulation study

We study the kinetic pathways for the isotropic-to-nematic transition in a fluid of colloidal hard rods. In order to follow the formation of the nematic phase, we develop a new cluster criterion that distinguishes nematic clusters from the isotropic phase. Applying this criterion in Monte Carlo simulations, we find spinodal decomposition as well as nucleation and growth depending on the supersaturation. We determine the height of the nucleation barrier and we study the shape and structure of the cluster. More specifically, we find ellipsoidal nematic clusters with an aspect ratio of about 1.7 and a homogeneous nematic director field. Our results are consistent with theoretical predictions on the shape and director field of nematic tactoids. Classical nucleation theory gives reasonable predictions for the height of the nucleation barrier and the critical nucleus size.     

Homogeneous two-dimensional nucleation of guest-free silicon clathrates

The difficulty in synthesizing guest-free semiconductor clathrates complicates the process of determining how these cage-like structures form. This work studies the microscopic mechanism of the nucleation of guest-free Si₁₃₆ clathrate using molecular dynamics simulations with the Stillinger–Weber potential. The homogeneous nucleation of Si₁₃₆, which is realized in a narrow negative pressure range before liquid cavitation, exhibits the characteristic feature of the two-dimensional (2D) mode. The critical nucleus is composed of one to two five-membered rings, and the nucleation barrier is close to 1 k_BT. According to a thermodynamic model based on atomistic nucleation theory, the effective binding energy associated with the formation of 2D critical nuclei is significantly low, which is responsible for the low nucleation barrier of Si₁₃₆ clathrate. In the post-nucleation period, the critical nucleus preferentially grows into a dodecahedron, and the latter continuously grows with sharing face along 〈1 1 0〉.     

Nucleation kinetics,growth and hardness parameters of l-alanine alaninium picrate (LAAP) single crystals

Amino acids are considered to be the building blocks of proteins and are gaining importance due to their interesting optical behavior. l-alanine is an amino acid which dissolves in water and it can react with other acids to form new compounds. In this work, l-alanine is mixed with picric acid to prepare l-alanine alaninium picrate (LAAP) salt. Solubility and metastable zone width were measured for LAAP salt and induction period was measured at different supersaturation ratios. The critical nucleation parameters were evaluated based on the classical theory of homogeneous nucleation. Using the optimized nucleation parameters, single crystals of LAAP salt were grown by slow evaporation technique. XRD and FTIR studies were carried out to understand structural and molecular formation of the crystal. Microhardness measurements were performed on the grown LAAP crystal and various parameters such as work hardening constant, stiffness constant, yield strength, resistance pressure and corrected hardness were evaluated. Nonlinear optical behavior of the sample was analyzed.     

Experimental study of boiling-up kinetics and superheat limit for n-hexane on solid powder-like structures

The experimental setup is described and results are presented for measuring average boiling-up lag time for superheated n-hexane mixed with solid structures (activated coal, cellulose, silica gel) as function of temperature under atmospheric pressure. The “aging” of the cell with the filler was carried out before measurements: this was about 600–1000 boiling events. We developed a new method for analysing of “aging” procedure: comparison of average flux (frequency) of boiling-up events (processing of experimental data) and the frequency of nucleation obtained from exponential model. By the end of aging of the cell with silica gel the average empirical flux reduces by factor of four relative to the “exponential” value. But for activated coal and cellulose the difference in these fluxes is about 20 %. In all experiments, the event flux was nonstationary. For n-hexane in tested systems, the margin of superheating was T _n/T _cr ≅ 0.873–0.875, although it was T _n/T _cr ≅ ≅ 0.883 for n-pentane in systems filled by nickel powder (sintered porous nickel with grains of 1.5 or 5.0 micron size) and in the presence of a smooth copper plate. The average time of boiling-up lag in n-hexane at low normalized temperatures was also smaller than for n-pentane. For all systems, the lag time is almost the same for the temperature range T _n/T _cr ≅ 0.860–0.874 (plateau). Thus, a smaller amount of superheated liquid or its division into smaller liquid elements does not result in longer liquid lifetime for superheat liquid and the maximal superheat temperature, as one could expect from the classical theory of homogeneous nucleation. Research was supported by the RF Presidential Foundation (NS-905.2003.2) and Russian Foundation for Basic Research (Grant No. 04-02-16285).     

基于Wenzel模型的粗糙界面异质形核分析

异质形核是形核发生的主要形式. 经典形核理论对基底界面作了理想化平面假设,然而实际异质形核体系中理想平直的固体界面是不存在的,这导致了异质形核描述与实际情况的偏差. 考察了固相晶胚在非平整界面上的异质形核过程,基于Wenzel润湿模型,分析了非理想界面的粗糙度因子对固相晶胚形核功的影响规律. 结果表明:当基底与晶核之间的本征润湿角小于90°时,基底界面越粗糙越有利于形核;本征润湿角大于90°时,基底界面越粗糙越不利于形核. 同时,游离晶胚在基底上润湿是球冠晶胚形成的重要途径,粗糙界面润湿过程中界面自由能的 关键词： 异质形核 粗糙界面 Wenzel模型 润湿过程     

Quantitative parameter-free prediction of simulated crystal-nucleation times

We present direct comparisons between simulated crystal-nucleation times and theoretical predictions using a model of aluminum, and demonstrate that a quantitative prediction can be made. All relevant thermodynamic properties of the system are known, making the agreement of our simulation data with nucleation theories free of any adjustable parameters. The role of transient nucleation is included in the classical nucleation theory approach, and shown to be necessary to understand the observed nucleation times. The calculations provide an explanation on why nucleation is difficult to observe in simulations at moderate undercoolings. Even when the simulations are significantly larger than the critical nucleus, and when simulation times are sufficiently long, at moderate undercoolings the small concentration of critical nuclei makes the probability of the nucleation low in molecular dynamics simulations.     

Non-uniformities in polymer/liquid crystal mixtures

We theoretically model the nucleation of nematic droplets during phase ordering in mixtures of a flexible polymer and a low-molecular-weight liquid crystal. By appealing to classical nucleation theory (CNT), we calculate the energy barrier to nucleation and the size of a critical nucleus. We study the influence of a metastable intermediate phase on the nucleation of the nematic. Below a triple point in the phase diagram, there are two distinct mechanisms for the formation of a nematic nucleus: 1) direct nucleation from the isotropic phase and 2) nucleation via a precursor metastable isotropic phase. We calculate the crossover concentration as a function of temperature, delineating the regions of the phase diagram in which each mechanism prevails. In the latter case, the presence of a hidden metastable isotropic-isotropic binodal may either promote or delay the nucleation of a nematic phase. Received 9 August 2002 RID="a" ID="a"e-mail: matuyama@chem.mie-u.ac.jp     

Attainable superheat of ethane-methane solutions

Methods of measuring lifetime and continuous pressure decrease were used to study kinetics of spontaneous boiling-up of superheated ethane-methane solutions. The attainable superheats of solutions at two pressure values (1.0 and 1.6 MPa) and two concentrations of methane (2.1 and 6.0 mole %) were determined experimentally in the range of nucleation rate J = 1·10⁴–3·10⁸ s^?1m^?3. At temperatures 266.5, 270.0, and 273.15 K, the attainable stretching of the studied solutions was measured. The experimental results were compared with the theory of homogeneous nucleation. At nucleation rates J ≥ 2.5·10⁶ s^?1m^?3, there is a fair agreement of the theory and experiment. The discrepancy in attainable superheat temperatures T _n does not exceed 0.8 K. It is shown that significant underheating of solution to theoretical values T _n at J < 2.5·10⁶ s^?1m^?3 cannot be bound only with heterogeneous nucleation but is conditioned by other factors as well.     

Suppression of ice nucleation in supercooled water under temperature gradients

Understanding the behaviours of ice nucleation in non-isothermal conditions is of great importance for the preparation and retention of supercooled water. Here ice nucleation in supercooled water under temperature gradients is analyzed thermodynamically based on classical nucleation theory (CNT). Given that the free energy barrier for nucleation is dependent on temperature, different from a uniform temperature usually used in CNT, an assumption of linear temperature distribution in the ice nucleus was made and taken into consideration in analysis. The critical radius of the ice nucleus for nucleation and the corresponding nucleation model in the presence of a temperature gradient were obtained. It is observed that the critical radius is determined not only by the degree of supercooling, the only dependence in CNT, but also by the temperature gradient and even the Young's contact angle. Effects of temperature gradient on the change in free energy, critical radius, nucleation barrier and nucleation rate with different contact angles and degrees of supercooling are illustrated successively. The results show that a temperature gradient will increase the nucleation barrier and decrease the nucleation rate, particularly in the cases of large contact angle and low degree of supercooling. In addition, there is a critical temperature gradient for a given degree of supercooling and contact angle, at the higher of which the nucleation can be suppressed completely.